On the circulant matrices with Ducci sequences and Fibonacci numbers

A Ducci sequence generated by A = (a1,a2,...,an)ϵ Zn is the sequence {A,DA,D2A,...} where the Ducci map D : Zn → Zn is defined by D(A) = D(a1, a2,...,an) = (|a2-a1|, |a3-a2|,..., |an-an-1|, |an-a1|). In this study, we examine some properties of the matrices Cn, DCn, D2Cn; where Cn =Circ(c0,c1,..., cn-1) is a circulant matrix whose entries consist of Fibonacci numbers.